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mathslover

  • 2 years ago

Prove that if the 3 altitudes of a triangle are equal then the triangle is equilateral. See attachment

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  1. mathslover
    • 2 years ago
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    I tried to do this and have got so far that AB = AC

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  2. mathslover
    • 2 years ago
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    @ParthKohli

  3. mathslover
    • 2 years ago
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    @experimentX

  4. mathslover
    • 2 years ago
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    I took following triangles :ABF and AEC by AAS I got both of these triangles congruent and therefore by CPCT AB = AC

  5. mathslover
    • 2 years ago
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    (CPCT = Congruent Parts of Congruent Triangles are equal)

  6. joemath314159
    • 2 years ago
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    That idea should work to get that AB=BC as well.

  7. mathslover
    • 2 years ago
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    So far , we have got ABC as isosceles. Now, I took triangle ABC and AFC both of these triangles are congruent by RHS BF = FC ( by CPCT ) therefore F is mid point of BC an AF is median and altitude also Therefore , this is the property of an equilateral triangle , so ABC is an equi. triangle

  8. mathslover
    • 2 years ago
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    Is this correct?

  9. mathslover
    • 2 years ago
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    You mean to take ABE and BEC triangles @joemath314159 ?

  10. joemath314159
    • 2 years ago
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    yep. and do exactly what you did with the other triangles again.

  11. mathslover
    • 2 years ago
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    I meant this : ADC and ABD in the above comment.

  12. mathslover
    • 2 years ago
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    OK wait..

  13. mathslover
    • 2 years ago
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    I think I had tried that earlier but I didnt' get any favorable result , wait let me do it again

  14. joemath314159
    • 2 years ago
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    there are many combinations you could take. The pair I see is triangles BEC and BDA.

  15. mathslover
    • 2 years ago
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    Oh yes that will work ... BEC and BDA .. this gives some output to me.

  16. mathslover
    • 2 years ago
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    Thanks a lot @joemath314159 for your help .. Might gonna work in more concentration for me..

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